There is a hitch-receiver tire carrier that I have seen advertised somewhere. It essentially extends the coach's receiver; the tire rides between the coach and the toad. You probably can use it without a toad.

We are planning of doing Alaska next summer and I want to carry an unmounted tire. The basement has filled up quickly however and I sort of hate to give up space for a very large Tire. I am now considering carrying it on top of the Jeep.

Like several others, I carry mine underneath, just ahead of the rear axle. I fabricated a simple H frame to ride between the frame rails and suspend a mounted tire from it. You can do a search for "spare tire" and you should come up with a couple of threads from two or three years ago.

This Spare Tire Thread from a couple years ago shows how I came up with a rack to carry a spare tire mounted underneath our motorhome. The mount works out real well as you don't loose any storage by trying to use a compartment.

There is an open area of the frame behind the fuel tank on our Journey where the spare mounts up against the frame rails. You can see the area and the tire from the compartent where the LP tank is.